Speaker
Description
Spherical observations arise in a variety of scientific disciplines, most notably in medical imaging, and yet the regression models for responses on the sphere remain relatively underdeveloped. A particular shortcoming of the existing literature lies in the absence of a rigorous framework for statistical inference. Many proposals emphasize model flexibility at the expense of theoretical tractability, while others rely on tangent-space approximations that undermine the validity of inference. In this paper, a generalized linear model for spherical responses is proposed, which is based on a canonical reparameterization of the von Mises–Fisher distribution that casts the model into the exponential family form. This formulation permits likelihood-based inference to be developed in a principled manner. Under mild regularity conditions, it is shown that the maximum likelihood estimator is consistent and asymptotically normal. A projection-based inference procedure is further developed, in which the estimated regression coefficient is decomposed into components parallel and orthogonal to the estimated mean direction, yielding asymptotically valid Wald tests for the directional and concentration effects separately. The robustness and power advantages of the proposed method over conventional procedures are confirmed through Monte Carlo simulations, and its practical utility is illustrated through an application to a LP-ds-rep dataset.